LinearGraph Wiki
Welcome to the LinearGraph Wiki by Lamar Edghill This Wiki seeks to allow students to learn how to effectively know and understand the concept of graphs, and to display a good level of competence in computations involving linear graphing. Describe your topic This Wiki will look mainly at: #what a linear graph is #what a linear equation is # How to plot a linear graph Linear Graph Linear relationships are used in everyday life. These relationships can be expressed in many differents ways. A linear graph is a series of points, discrete or continous, as in forming a straight line each of which represents a value of a given function. These values of the function are called variables. A quantity whose value can change is known as a variable. Functions are used to describe the rules, which deﬁne the ways in which such a change can occur. These functions are known as the equation. A linear equation is an equation for a straight line. Linear Equations A linear equation is an equation whose graph is a straight line. A linear equation in one variable is an equation that simlpy involves x. There are no terms involving x2, x3, x1/2 etc. Each term has a degree of at most 1. All operations, such as addition or multiplication, involve only x and numerical constants. 3x + 4 = 5 is an example of a linear equation. 2(x+1) = 6(x-4) is also a linear equation. These equations can be solved very easily by performing algebraic operations to the equation to isolate x. A linear equation in two variables is, as the name suggests, an equation that involves 2 variables. The standard form of this type of equation is Ax + By = C, where A,B and C are real numbers. For example, 3x + y = 7 is a linear equation in two variables. y = 2x + 1/3 is also an example, since it can be rewritten as 2x - y = -1/3 ( or equivalently 6x - 3y = -1 ). Domain and Range When working with functions, we frequently come across two terms: DOMAIN & RANGE. What is a domain? What is a range? Why are they important? Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work. Range: The range is the set of all possible output values (usually y), which result from using the function formula. Summary: The domain of a function is all the possible input values, and the range is all possible output values. Plotting a straight line graph: Linear graphs are one way of expressing these relationships, when graphed they give a straight line. Linear graphs can be sketched or plotted ' *Use graph paper or grid paper for accuracy. *Use X and Y as variables. *Give values to X and work out the values of Y, set these values in a table. *Place the axes in the most suitable position, to give the best presentation of the graph. *Choose a suitable scale. *Plot the points from your table of values. *Join the points to give a straight line. Example Sketch the linear equation y = 2''x'' +3 , using the x- and y- intercepts. To find the x-intercept, let y=0 When y=0, 2''x'' +3 = 0 2''x'' = -3 x'' = -3/2 = -1.5 Now we can write the co-ordinates of the x-intercept as (-1.5,0) '''To find the y-intercept, let ''x = 0''' When x = 0, y = 2 x 0 y = 3 Reference Linear Graph. (n.d.). Retrieved 31 March, 2013 from http://www.staff.vu.edu.au/mcaonline/units/graphs/linear.html Nipissing University. (n.d.). Linear Equation Tutorial. Retrieved 31 March, 2013 from http://calculus.nipissingu.ca/tutorials/linear.html Category:Browse